Doppler array with plural slotted waveguides and feed switching



Sept. 27, 1966 A. J. SIMMONS 3,276,026

DOPPLER ARRAY WITH PLURAL SLOTTED WAVEGUIDES AND FEED SWITCHING Filed May 10, 1962 5 Sheets-Sheet l F INVENTOR.

ALAN J. SIMMONS BY W%) q} l d/MM ATTORNEYS Sept? 27, 1966 A. J. SIMMONS 3,276,026

DOPPLER ARRAY WITH PLURAL SLOTTED WAVEGUIDES AND FEED SWITCHING Filed May 10, 1962 5 Sheets-Sheet 2 I M In INVENTOR. ALAN J. SIMMONS BY W OW) w P ATTORNEYS Sept. 27, 1966 A. J. SIMMONS 3,276,026

DOPPLER ARRAY WITH PLURAL SLOTTED WAVEGUIDES AND FEED SWITCHING 5 Sheets-Sheet :5

Filed May 10, 1962 INVENTOR. ALAN J. SIMMONS BY W ATTORNFYQ United States Patent OfiFice 3,276,026 DOPPLER ARRAY WITH PLURAL SLOTTED WAVE- GUIDES AND FEED SWITCHING Alan J. Simmons, Winchester, Mass., assignor, by mesne assignments, to Laboratory for Electronics, Inc., Boston, Mass., a corporation of Delaware Filed May 10, 1962, Ser. No. 193,717 2 Claims. (Cl. 343-768) This invention relates in general to antennas and more particularly to an array of elements for radiating high frequency electromagnetic energy so that the energy is confined to form a highly directional beam.

Airborne Doppler navigation systems are known which employ an antenna for transmitting a plurality of independent, highly directional beams toward the surface of the earth. One method found suitable to accomplish this result is to utilize a wide angle lens employing a plurality of separate feed horns, each feed horn causing a beam to be radiated in a direction which is fixed relative to the other beams. The wide angle lens arrangement gives excellent results, but is rather bulky and requires much space in an aircraft.

The primary object of the invention is to provide an array of radiating elements for transmitting a plurality of independent beams whose directions are fixed relative to one another. An advantage of the invention is that the array may be placed in an aircraft where it will take up 'less space than is required for the wide angle lens arrangement. Further, each of the radiated beams has low side lobes and a gain only slightly less than would be expected from an antenna of aperture size equal to that of the entire array.

The invention resides in a beam-forming antenna having a pair of feed waveguides arranged to permit input energy to be applied at any one of four ports. Interconnecting and coupled to the feed waveguides by means of slots in the feed waveguides are a plurality of radiating waveguides. Each radiating waveguide has a plurality of slots through which radiates beam-forming electromagnetic energy. Switches are arranged so that when a signal is transmitted to one of the input ports of the feed waveguides, the other input ports are terminated in a matched load. The energy passing through the slots forms a single beam whose direction is dependent upon which input port is energized. Physically, the array is a symmetrical structure and the beam positions are symmetrically located with respect to the vertical axis of symmetry of the array.

The invention will be more fully understood from the following description when taken in connection with the appended drawings wherein:

FIG. 1 depicts the planar array and the beams radiated thereby;

FIG. 2 shows an orthographic view of the array showing the assemblage of radiating guides extending between the two feed guides;

FIG. 3 illustrates the arrangement of slots in the radiating guides;

FIG. 4 shows an arrangement for transferring energy between the feed guide and the radiating guides; and a FIG. 5 illustrates a switching arrangement for feeding microwave energy through a selected port to the array.

Referring now to FIG. 1, there is depicted a planar antenna array which customarily is mounted horizontally in an aircraft so that when the aircraft is in strai ht and level flight, the radiated beams are directed downwardly toward the earth. The array is symmetrical with respect to orthogonal axes X, Y, and Z. A pencil beam, which may assume any of the positions indicated by the beams 11, 12, 13, or 14, is radiated from the array dependent upon which one of four input ports of the array is eneraz'zaaze Patented Sept. 27, 1966 gized, as well be explained hereinafter. The term pencil beam may be defined as a highly directive antenna pattern consisting of a single major lobe contained within a cone of small solid angle and almost circularly symmetrical about the direction of peak intensity. The beams 11, 12, 13, and 14 are located at an angle 0 with respect to the vertical axis Z and with respect to the horizontal X axis.

Referring now to FIGS. 2 and 3, the planar array 10 is depicted in greater detail. A pair of feed waveguides 21 and 22 are shown, each having a pair of input ports 31, 32, 33, and 34, respectively. The ports have flanges 31a, 32a, 33a, 34a, allowing the input ports to be connected to a source of energy, or, alternatively, to a reflectionless terminating device.

Disposed between the feed waveguides 21 and 22 and coupled thereto are a plurality of radiating waveguides 41 designed to transmit the beams 11, 12, -13, 14 of FIG. 1. All the radiating waveguide-s 41 are identical, and each radiating waveguide has a multiplicity of slots 45 cut through the waveguide wall. The slots are uniformly spaced along the guide and are arranged so that the slots on one side of the YY axis, except for the central slot through which the YY axis passes, are identical to the arrangement of the slots on the opposite side of the YY axis, that is, as one proceeds outwardly from the center slot in both directions, slots which are equidistant from the center slot have the same angle of inclination. The angle of inclination of the slot determines the proportion of the energy in the guide at the slot which is radiated. Theoretically, an infinitely thin slot whose longitudinal extent is perpendicular to the direction of wave propagation does not radiate wave energy. The slots 45 closest to the guides 21 and 22 are almost perpendicular to the longitudinal axis of the guide 41 and therefore radiate very little energy. The slots alternate in their direction of inclination, thereby providing the correct phase relationship between the slots.

Referring now to FIG. 4, there is depicted the junction of the feed waveguides 21 and the radiating waveguides 41. The feed waveguide 21 (the feed waveguide 22 is identical to waveguide 21) is shown having a plurality of slots 25 whose centers are spaced by a distance d the slots 25 being similar to the slots 45 of radiating waveguides 41. The number of slots in waveguides 21 and 22 is dependent upon the number of radiating waveguides, each radiating waveguide 41 being coupled to the feed waveguides by means of the slots in the feed waveguide.

As can readily be seen, the waveguides 41 are mounted perpendicular to feed waveguide 21. Preferably, waveguides 41 are closed off at their ends. Each of the slots 25 (as well as slots 45 of the radiating waveguide) are cut a distance d into the 'broad wall of the waveguide. Energy coupled from the slots 25 enters the radiating Waveguides 41 and is radiated through slots 45.

As has been previously mentioned, the planar array 10 emits a pencil beam depicted as either 11, 12, 13, or 14 in FIG. 1. The beam which is radiated from the array is dependent upon which one of the four input ports 31, 32, 33, 34 is energized with microwave energy. The angle of the pencil beam emitted is a function of the spacing d of the slots along the feed waveguides 21, 22 and the spacing d of the slots along the radiating waveguides 41.

The general approach to the design of the array is similar in some ways to that used in The Eagle Scanner, as described in Radar System Engineering, Rad. Lab. Series, vol. 1, McGraw-Hill, 1947, pp. 291-295, where there is discussed a single, slot array antenna capable of being fed from either end. The Eagle array is designed as a traveling-wave array with the coupling coeflicients of the .ture.

z1 and 22.

slots in the first half of the array chosen to give equal power radiated from each slot. This means that the slot coupling increases toward the center of the array. The second half of the array is the image of the first half so that from the center outward the slot coupling falls oil. This decrease in coupling, plus the fact that the power traveling along in the waveguide continually decreases as a portion of it is radiated through each successively encountered slot, means that the power radiated from each slot falls off rapidly from the center to the end of the array, in a roughly exponential fashion. Thus, the amplitude distribution of the energy radiated along the array is asymmetrical, although the slot coupling is symmetrical. The resulting pattern of this asymmetrical distribution as compared to the pattern of a uniform distribution produces a somewhat wider beam width, filled-in nulls, and slightly lower side lobesdb rather than the 13 db one would expect from uniform distribution. As an aid .to understanding this resulting pattern, the amplitude distribution over the array is viewed as the sum of two distributions, one symmetrical and the other antisymmetrical about the center. The radiation pattern of the total array distribution may be calculated, by use of superposition, as the sum of the radiation patterns of these two distributions. The symmetrical distribution produces a main beam with side lobes somewhat below 13 db because of the amplitude taper. The antisymmetrical distribution produces a split beam pattern, with a null in the direction of the principal beam of the symmetrical distribution. The peaks of the lobes of this split beam pattern occur at the positions of the nulls in the pattern of the symmetrical distribution and are in phase quadra- Thus, to a first approximation, the antisymmetrical distribution tends to fill in the nulls, perhaps to reduce the gain and widen the beam width slightly, but has little effect on raising the side lobes generally.

The design technique used in The Eagle Scanner can be further extended by choosing amplitude distributions over the first half of the array other than the uniform distribution. Further, the coupling values can be chosen so that the symmetric parts approximate distributions which are known to give low side lobes, such as Tohebycheff distributions. While no general theory of low side lobe distributions of this type has been Worked out, several possible low side lobe distributions have been discovered with the aid of machine-computed patterns.

The spacing of the slots along the radiating waveguides d and along the feed waveguides d is determined in the following manner: The array of identical parallel waveguides 41, with radiating slots 45, are fed from either end by means of coupling slots from feed waveguides The complex amplitude of the voltage in any slot at position (x,y) may be expressed as the product of two functions:

where 0,; and 9,. are angles measured from the X and Y axes of the array respectively.

The equations transforming from 0, coordinates to 0 0 coordinates are:

cos 0 =cos sin sin 6 The pattern Gte is that of an array of isotropic sources along the X axis with amplitude g(x), and H (0 is the pattern due to an array with distribution h:(y).v Because of the separation of the total pattern into the product of cos 0 =sin sin 6 two simpler pat-terns, it is easiest to consider these simpler patterns separately, that is, to design the individual radiating waveguides 41 and the feed waveguides 21, 22 as ordinary linear arrays and then combine them to get the total pattern desired.

Some consequences of the fact that the pattern of the array is the product of the two linear patterns is that if each linear .array has only one main beam, occurring at angles 0; and 0,, which define two cones in space, then the main beam of the whole array occurs along the intersection of the two cones. Furthermore, the only appreciable side lobes must occur on these cones too, where the main beam of one linear array multiplies a side lobe of the other. The side lobes are thus restricted to certain regions in space, and in general, no side lobes appear at direct-ions close to the Z axis, a fact of great benefit for overwater Doppler navigation systems.

In the present application, the beam maxima should occur at values of 0=21i1 and =i45, i (only three of the four possible beams are actually used in the system). From Equations 3 and 4, the values of 9; and 6 may be determined, as shown in Table I.

TABLE 1 Beam Number 9 d 6; 0;

In order to obtain the desired values of 0 and 6f, we must have, as is well known from array theory, a linear phase variation along the x and y axes:

s"( )=l )l (y)=l )l y where :2 and a are constants given by 0 a1- M cos 0 (7) 21; O a,, cos 0,, (8)

where x and y are distance coordinates along the X and Y axes, respectively, and where a is the free-space Wavelength of the microwave energy used.

It may be seen that cos (75.321")=-oos(104.679) so that in order to go from beam 1 to beam 2, for example, it is merely necessary to reverse the sign of a This may be readily done by reversing the end at which the feed waveguides 21 or 22 are fed.

In order to find the spacing for a uniformly spaced array of slots whose phase is alternated in, we have that the coordinate of the nth slot of the radiating waveguide is where n is the number of slots along the waveguides 41 and where d is the slot spacing and its phasing must be From (7) and (11), the expression for d may be found:

l l cos 0 df x. M (13) Amplitude distribution The amplitude distribution of the power radiated from each of the slots and determines the beam width and side lobe level of radiated beam. Power transferred from each of the slots 25 of the feed waveguides 21, 22 and the slots 45 of the radiating waveguides 41 to give a desired beam width and side lobe level are determined empirically by trial and error.

A possible method of selecting the power distribution of the radiation from each slot and the one used in the present embodiment of the invention is to distribute the coefiicient of coupling of the slots 25 and 45 up to the central slot of each waveguide according to the formula where n is the slot number along the feed waveguide or the radiating waveguide, N is the total number of slots in the feed Waveguide or the radiating waveguide, and D is a constant, generally within the range from 0 to about 1 to be determined by trial and error.

It has been found that the addition of the constant D to the function in Equation 14 narrows the beam Width and decreases the maximum value of coupling, both desirable effects, while producing the undesirable effect of raising the side lobe level slightly.

Since the array is symmetrical, once the coefiicient of coupling for the slots up to the central slot is determined, the parameters of the slot such as slot angle and slot depth are chosen for the slots up to the central slot, and then the remaining slots are given similar parameter values.

Of course, other distributions of coupling coeflicients may be used rather than that of Equation 14. For example, Tchebycheif distributions could be used. However, it has been found that such a distribution provides too high a side lobe level.

As an example, for an array having twenty-one radiating waveguides, each Waveguide having thirty-five slots, the constant D was chosen to be 0.03. After traversing the radiating waveguide, the power remaining at the end of each radiating waveguide 41 was 0.177 of the power entering the radiating waveguide. For each radiating waveguide, the formula for determining the correct power from each slot from Formula 14 becomes g(n)=sin g g-F003 and for the feed waveguides:

Design of radiating waveguide slots The slot depth and slot angle for each slot is determined empirically after determining the correct value of g(n) from Formula 15. In order that the phase velocity of the wave energy propagating in the radiating waveguides 41 be unaffected by the radiating slots, it is necessary that the slots 45 be resonant, that is, have zero reactance. A method of determining the resonant length of slots with non-resonant spacing is disclosed by W. H. Watson in Waveguide Transmission and Antenna Systems, Chapter VIII.

It has been found that the length of the slot at resonance measured on the outside of the waveguide is essentially independent of slot angle. This fact has made it possible to formulate an "analytic expression relating slot angle and depth as:

where L is equal to the length of the slot at resonance, d is equal to the depth of the slot, and a is equal to the slot angle. The expression (17) holds true for values up to oc=25. For the thirty-five slots of each radiating waveguide, each slot being 0.040 inch wide, alternately inclined, spaced 0.4635 inch apart, and symmetrical about the center slot, the values of slot angle on and slot depth d are given below. The waveguide used for the radiating waveguides and the feed waveguides was K -band waveguide, having internal dimensions of 0.311" x 0.622" and the frequency of the input power to the array TABLE I11 FIRST RADIATIN G (35 ELEMENT) ARRAY n-slot number 0LSl0l2 angle, dr'slot depth degrees Design of feed waveguide slots The slot depth and slot angle for each slot is determined empirically after determining the correct value for each slot of g from Formula 16. Since the slots in the feed waveguide are isolated from each other by the radiating waveguide to which they vare coupled, it is possible to detclirmine the parameter of the slots by examining single s ots.

Coupling of the feed slots was determined from measurements on T-s" comprising a feed waveguide coupled by a slot to a radiating waveguide as shown in FIG. 4. Data for determining the susceptance of the slot was obtained by alternately placing a short circuit and an open circuit across the slot and noting the change in position of a field strength minimum on a slotted line for each of these conditions. The slot length for zero susceptance is independent of slot angle as in the case of the radiating slots, and the analytic expression (17) relating to slot angle and depth for the feed waveguide was the same as for that for the radiating waveguides. However, for the feed waveguides, the expression (17 was found to hold true for values of slot angle (,8) up to 13:32".

For the twenty-one slots of each feed waveguide, each slot being 0.040 inch wide, alternately inclined and spaced 0.4635 inch apart, and symmetrical about the center slot, the values of slot angle 5 and slot depth d are given below.

TABLE IV FIRST FEEDING (21 ELEMENT) ARRAY nslt number Bslot angle, dnslot depth degrees 1, 21 +4. 4 116 2, 20 -ti. 2 1155 3, 19 +8. 3 1145 4, 18 10. 5 1130 5, 17 +12. 7 1115 6, 16 l5. 0 1005 7, +17. 1 1075 8, 14 19.4 1050 9, 13 +21. 9 1015 10, 12 24. 2 0980 ll +27. 0 0925 While the antenna. thus far described has been designed for a specific frequency of 13.325 G.C., the antenna could be used at a frequency range of approximately 13.00 to 13.65 G.C. By modification of the dimensions of the Waveguides and slot, the antenna could be designed to operate in a frequency range of from 1,000 to 100,000 rnegacycles.

Referring now to FIG. 5, there is depicted a general arrangement of the switching circuit of the array of FIGS. 1-4. The switching circuit of FIG. 5 includes a circulator 88. A circulator is a non-reciprocal device which couples electrical signals to successive output terminals. The fourport circulator 88 has a source 82, a matching termination 84, a receiver 86, and an output rectangular waveguide 92 connected to each of its four ports. Energy from source 82 is fed to one of three output ports 98, 102, 104 of the switching circuit which are respectively connected to three of the ports of feed waveguides 21, 22 of FIGS. 2 and 3. Energy from source 82 is fed into rectangular waveguide 92 via the circulator 88 and enters a polarization rotator 96 via a rectangular-to-circular waveguide transition section 93a. A polarization rotator, the properties of which are well known, can be realized at microwave frequencies by the use of ferrites as is depicted in FIG. 5. The electric field vector of microwave energy in the rotator 96 is perpendicular to the resistive sheet 94, and the energy is passed through the sheet 94 unattenuated. If the waveguide 98 is to receive the energy from source 82, rotator 96 is biased to provide zero degrees rotation and all of the energy in the rotator enters waveguide 98. If, however, waveguides 102 or 104 are to receive the energy, the rotator 96 is biased to provide a 90 rotation and all the energy will pass to a second rotator 99 via a pair of circular-to-rectangular waveguide transitions 93b, 93c, and a rectangular waveguide 95. The electric field of microwave energy entering rotator 99 is perpendicular to resistive sheet 97 and passes through the sheet 97 unattenuated. The energy then passes through the rotator 99 and is rotated either 0 or 90, depending upon which waveguide, 104 or 102, is to receive the energy.

Referring again to FIGS. 2 and 3, the array is designed to transmit three beams, and, therefore, one of the ports -31, 32, 33, 34 is terminated with a matched load at all times. If the ports 31, 32, and 33 are connected to waveguides 98, 102, and 104, respectively, and port 34 is terminated at all times with a matched load, when the 'port 31 is excited with energy from waveguide 98, a

small portion of this energy feeds into ports 32, 33, and 34 through the array since all of the energy is not completely coupled by the slots 45. Naturally, any energy at the port 34 is absorbed by the matched load terminating the waveguide. If the rotator 99 is biased to provide 0 rotation, energy entering waveguide 102 from array port 32 isparallel to resistive sheet 97 and is absorbed thereby. However, energy entering waveguide 104 from port 33 passes unattenuated by the sheet 97 and is absorbed by resistive sheet 94 since the electric field vector polarization of the microwave energy is parallel to sheet 94. Conversely, if either port 32 or 33 is excited with energy from source 82, energy entering the remaining two guides from the array is absorbed by resistive sheets 94 and 97.

Obviously, many modifications and variations of the present invention are possible in the light of the foregoing teachings. It is to be understood, therefore, that the invention is not limited in its application to the details of construction or arrangement of parts specifically described and illustrated, and that within the scope of the appended claims, it may be practiced otherwise than as specifically described or illustrated.

What is claimed is:

1. A planar antenna for converting microwave energy from a source thereof into a shaped beam directed at an acute angle with respect to the radiating surface of such antenna, comprising:

(a) a parallel array of identical slotted radiating waveguides, the coupling coeflicient of the radiating slots in each such waveguide varying in accordance with the following formula:

where n is the number of any radiating slot from either end of the radiating waveguides toward the center thereof; N is the total number of radiating slots in any one of the radiating waveguides; and, D is a constant from 0 to about 1; and

(b) coupling means for energizing the planar array with microwave energy from a source thereof, said coupling means including:

(1) a first and second waveguide parallel to each other and coupled, respectively, by coupling slots to the first and the second end of each one ofthe radiating guides, the coupling coefiicient of each coupling slot between each of the first and the second wavegiide and each one of the radiating waveguides varying in accordance with the following formula:

where n is the number of any coupling slot between the first and the second waveguide and a radiating waveguide from either end of the first and the second waveguide toward the center thereof; N is the total number of radiating waveguides; and D is a constant from 0 to about 1; and

(2) means for connecting the source of microwave energy successively to the difierent ends of the first and the second waveguide.

2. A planar antenna as in claim 1 wherein the depth of each radiating slot and each coupling slot is:

respect to the longitudinal axis of its supporting wave guide.

References Cited by the Examiner UNITED STATES PATENTS 2,932,823 4/1960 .Beck et al. 343- 771 2,967,301 1/1961 Rearwin 343-477 3,020,549 2/1962 Kales 343 -771 3,078,463 '2/1963 Lamy 343 771 3,135,959 6/1964 Moran 343-771x FOREIGN PATENTS 837,091 6/1960 Great Britain.

HERMAN KARL SAALBACH, Primary Examiner. E. LIEBERMAN, W. K. TAYLOR, Assistant Examiners. 

1. A PLANAR ANTENNA FOR CONVERTING MICROWAVE ENERGY FROM A SOURCE THEREOF INTO A SHAPED BEAM DIRECTED AT AN ACUTE ANGLE WITH RESPECT TO THE RADIATING SUFACE OF SUCH ANTENNA, COMPRISING: (A) A PARALLEL ARRAY OF INDENTICAL SLOTTED RADIATING WAVEGUIDES, THE COUPLING COEFFICIENT OF THE RADIATING SLOTS ING EACH SUCH WAVEGUIDE VARYING IN ACCORDANCE WITH THE FOLLOWING FORMULA: 